All Questions

This is a generalization of the following question by John Wiltshire-Gordon. Consider an inductive family of finite groups: $$ G_0 \hookrightarrow G_1 \hookrightarrow \ldots \hookrightarrow G_i \...

Standard setup. Consider a group and choose generators. Word-metric (or in the other words - distance on the Cayley graph of the group+generators) - converts a group into a metric space, which is ...

In wonderful lectures by P. Diaconis "Group representations in probability and statistics, Chapter 6. Metrics on Groups, and Their Statistical Use" metrics on permutation groups are considered and ...

Let $G$ be a finite group, and let $Q$ be a probability measure on $G$. Suppose that $Q$, as a function on $G$, is supported on a conjugacy class $C$. We denote by $Q^{*k}$ the $k$-fold convolution of ...

$\DeclareMathOperator\Cov{Cov}$Motivation: If $G$ is a finite group and $\phi=X+iY: G\to \mathbb{T}$ is a character of $G$, then $\Cov(X,Y)=0$ where $X$, $Y$ are considered as two real random ...

Terry Tao gives this oblique definition of quasirandom group in his notes 3 $G$ is quasi-random (of order $D$) if all non-trivial unitary representations $\rho: G \to U(H)$ have dimension at least $...